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Published online by Cambridge University Press: 28 October 2019
In this chapter we introduce the endpoint map thatassociates a control function $u$ with the finalpoint of the admissible trajectory associated with$u$ and starting from a given point. This viewpointpermits us to interpret candidate abnormallength-minimizers as critical points of the endpointmap. It is then natural to introduce Lagrangemultipliers. First-order conditions recoverPontryagin extremals, while second-order conditionsgive new information.
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